Since most jets can legally reverse under their own power, can prop airplanes do the same? I know pilots are able to change the direction of the propellor to provide enough reverse thrust for slowing on landing roll, can they change even more to get it moving in reverse from a stop?

"But this airplane has 4 engines, it's an entirely different kind of flying! Altogether"

Turboprops can do it, but I don't know if any reciprocating engine has ever had reversing capabilities

Of course, in most cases I think it is against the manufacturer's guidance to use reverse pitch (beta range) below an established forward airspeed due to the risk of FOD damage to the prop or engine. However, it definitely comes in handy in certain situations; I recently saw a Caravan reverse back into a parking spot beside a grass runway because there was no ground equipment available to move him after shutdown. Needless to say, the owner of the clean little Experimental next to the Caravan was not very happy with having his shiny airplane covered in dust and grass afterwards

I remember sitting in an EMB-120 at BRU in 1993 when we pushed back from parking position under reverse with a marshaller infront of the aircraft guiding the cockpit crew ...
I could see the marshaller in front of the a/c (cockpit doors were not neccessarily closed then all the time) giving the cockpit crew directions during the power back ...

The Lockheed Constellation could easily back up on its own power as could the Bristol Britannia on which the F/E used to stand on his seat and stick his head up through the ditching hatch so as to check all was clear behind. No matter which aircraft you were on when backing it was always best for the pilots to keep their feet on the floor so they were not tempted to apply the brakes, which could possibly sit the aircraft on its tail

Grumman E2/C2 planes are commonly taxied backward using reverse thrust. You haven't learned how to taxi properly until you've learned how to back into a parking spot on an aircraft carrier that is just 4 inches wider than your prop arcs and stop with 1/2 the plane over the side of the ship (without falling over the side into the water).

Depends on the aircraft. Many can, many can't. HS-748 cannot; as the props can't actually reverse pitch, just go to essentially zero pitch (which still helps a lot on landing - as far as going fast in a forward direction goes zero pitch is about as helpfull as hanging a sheet of plywood off the front of the engine).

Many moons ago, when I was working at a repair station, we had a customer that had a C-182 that he had the Robertson STOL package installed on it. He also installed a fully reversible 2 blade prop on the C-182, so he would taxi up to the ramp, put it in reverse and back it into his tie down spot instead of pushing it back.

Unfortunately, there were many problems with the prop governor that came with the kit, and the factory was never able to correct the problem, so he reinstalled the original propeller and prop governor and returned the kit to the factory. I don’t remember if this kit was from Robertson or a third party.